Orthodoxy under the Soviet occupation
The religious policy of the Soviet occupation was state atheism — the aim was to eradicate religion. Yet the treatment was not equal: the Moscow-Patriarchate Russian Orthodox Church was instrumentalised and comparatively spared, while the autonomous Estonian Orthodox Church was crushed and the minority faiths' shrines and cemeteries were destroyed. That same double standard explains why the Russian Orthodox and main city cemeteries survived while the Tatar, Jewish, Baltic-German and Catholic ones did not.

The Alexander Nevsky Cathedral on Toompea hill in Tallinn, an Orthodox church with onion domes and towers (Diego Delso; CC BY-SA 3.0; Wikimedia Commons)
State atheism
The Soviet Union proceeded from a Marxist-Leninist ideology whose goal was to abolish religion and replace it with state atheism. Occupying Estonia in 1940, the authorities set about dissolving the churches' independence: congregations lost their legal standing, church property was nationalised, religious teaching was banned and the clergy repressed. This affected every faith — including the Muslim Tatars, whose two congregations were dissolved.
The subordination of the Estonian Orthodox Church
Before the occupation about a fifth of Estonians were Orthodox, and the Estonian Apostolic Orthodox Church had been autonomous under the Patriarchate of Constantinople since 1923 — 158 parishes, monasteries at Petseri and Kuremäe (Pühtitsa), two convents, a chair of Orthodoxy at the University of Tartu. In 1945 a representative of the Moscow Patriarchate dissolved the synod that had remained in Estonia and subordinated the Orthodox as a diocese of the Russian Orthodox Church. Metropolitan Aleksander went into exile in 1944 with 21 clergy and about 8,000 believers; most of the bishops and priests who remained were deported to Siberia.
An instrumentalised church
The Russian Orthodox Church itself (the Moscow Patriarchate), from Stalin's 1943 turn, became an instrument of the Soviet occupation authorities and was tolerated comparatively better. Tallinn's Alexander Nevsky Cathedral kept functioning throughout the Soviet occupation (though under atheist pressure). The Kuremäe (Pühtitsa) convent was marked for closure during Khrushchev's anti-religious campaign („unprofitable”, the building to become a sanatorium) but was in the end spared — so as not to damage the Soviet Union's image. Thus the great Russian Orthodox shrines and their cemeteries survived.
The double standard in cemeteries
Here the story meets ours. The Russian Orthodox and main city cemeteries — Tallinn's Alexander Nevsky (Inner City) cemetery — kept working, while the occupation authorities razed the minority congregations': the Tatars', Jewish, Baltic-German (Kopli, Mõigu) and Catholic. According to the Estonian Heritage Yearbook the larger cemeteries were destroyed „as a campaign and evidently with the deliberate aim of breaking cultural continuity” — precisely what was not done to the Russian Orthodox institutions.
See also
Sources: Wikipedia „Estonian Apostolic Orthodox Church”, „Alexander Nevsky Cathedral, Tallinn”, „Russian Orthodox Church”; OrthodoxWiki „Church of Estonia”; Estonian Heritage Yearbook (Muinsuskaitse aastaraamat) 2007 (the cemetery double standard).